Henrikh Mkhitaryan and Pierre-Emerick Aubameyang netted goals either side of half-time for Dortmund as Jürgen Klopp recorded a third win in five against Pep Guardiola's Bayern.
Dortmund dominated the game from start to finish and, like a year ago when they triumphed 4-2, drew first blood ahead of the official start to the 2014-15 season.
The match also marked former Dortmund striker Robert Lewandowski's return to the Westfalenstadion after his free transfer but, unlike Mario Göze, the striker could not mark his reappearance by the Ruhr with a goal.
At the opposite end, Aubameyang celebrated his clincher by donning a Spider-Man mask. He has since been christened Spiderbameyang.